Diagnostic and prognostic performance of Mxa and transfer function analysis-based dynamic cerebral autoregulation metrics

Abstract

Dynamic cerebral autoregulation is often assessed by continuously recorded arterial blood pressure (ABP) and transcranial Doppler-derived mean cerebral blood flow velocity followed by analysis in the time and frequency domain, respectively. Sequential correlation (in the time domain, yielding e.g., the measure mean flow index, Mxa) and transfer function analysis (TFA) (in the frequency domain, yielding, e.g., normalised and non-normalised gain as well as phase in the low frequency domain) are commonly used approaches. This study investigated the diagnostic and prognostic performance of these metrics. We included recordings from 48 healthy volunteers, 19 patients with sepsis, 36 with traumatic brain injury (TBI), and 14 patients admitted to a neurorehabilitation unit. The diagnostic (between healthy volunteers and patients) and prognostic performance (to predict death or poor functional outcome) of Mxa and the TFA measures were assessed by area under the receiver-operating characteristic (AUROC) curves. AUROC curves generally indicated that the measures were ‘no better than chance’ (AUROC ∼0.5) both for distinguishing between healthy volunteers and patient groups, and for predicting outcomes in our cohort. No metric emerged as superior for distinguishing between healthy volunteers and different patient groups, for assessing the effect of interventions, or for predicting mortality or functional outcome.

Introduction

Dynamic cerebral autoregulation dampens changes in cerebral blood flow during acute fluctuations in cerebral perfusion pressure (CPP) by adjusting cerebrovascular resistance. ¹ Dynamic cerebral autoregulation can be estimated in either the time or frequency domain. ² The mean flow index (Mx) was introduced by Czosnyka et al. in 1996 as a time-domain-based measure of dynamic cerebral autoregulation. ³ It is based on simultaneous recording of transcranial Doppler ultrasound (TCD)-based mean flow velocity in the middle cerebral artery (MCAv) and either cerebral perfusion pressure (CPP) or, in the absence of intracranial pressure (ICP) measurement, arterial blood pressure (ABP). ⁴ Before calculation, data are commonly pre-processed by dividing recordings into blocks, collating blocks into epochs, and using different durations of overlaps, if any. It is then calculated as the mean of the repeatedly calculated correlation coefficients either between MCAv and CPP or as the mean correlation coefficient between MCAv and ABP, ⁵ in which case it is referred to as Mxa. Both Mx and Mxa range from −1 to 1; high positive values indicate impaired dynamic cerebral autoregulation, and conversely low values reflect more intact autoregulation. ³ The predominantly used threshold between preserved and impaired cerebral autoregulation is 0.3. ⁶ The diagnostic performance of Mxa has previously been assessed by averages between different patient groups. Actual prediction modelling has only been reported for stroke patients with healthy volunteers as comparators, showing low (area under the curve, AUC 0.5–0.7) to moderate accuracy (AUC 0.7–0.9).7,8 The prognostic performance of Mx and Mxa have been investigated in patients with traumatic brain injury (TBI), subarachnoid haemorrhage, and sepsis with results ranging from ‘no better than chance’ (AUC of ∼0.5) to moderate accuracy depending on the diagnosis and specific outcome.^5,9–12

Similarly to Mx and Mxa, transfer function analysis (TFA) is a measure of dynamic cerebral autoregulate. However, TFA is a frequency domain-based approach, where spontaneous oscillations in pressure (e.g. ABP) is considered the input and MCAv is considered the output. ¹³ By this method, dynamic cerebral autoregulation is commonly assessed by tranfer function gain, phase, and coherence in the low frequency domain (0.07–0.20 Hz), ¹³ where an increase in phase and a decrease in gain are usually interpreted as improvement of dynamic cerebral autoregulation.^13,14 The prognostic performance of TFA reportedly has moderate accuracy for patients with TBI. ¹² However, neither diagnostic or prognostic performance has been investigated using the recommended standardised methodogy. ¹³

In the present study, we investigated and compared he diagnostic and prognostic performance of Mxa and TFA. The diagnostic performance was investigated by comparing a group of healthy volunteers to patients with sepsis, patients with TBI, and patients admitted to a neurorehabilitation unit after traumatic or non-traumatic brain injury, respectively. Previous reports have shown some impairment of dynamic cerebral autoregulation in these three patient categories.^13–16 The prognostic performance was investigated by comparing clinical outcomes for patients with sepsis and TBI. Since there is no consensus on the approach of pre-processing for Mxa, the diagnostic and prognostic performance was investigated using four pre-processing approaches that have previously been reported in the literature^6,17,18 while TFA was assessed in accordance with current recommendations. ¹³

Methods

Ethical approval

The present retrospective work is based on data from five studies, which have previously been published elsewhere,^18–23 and describes entirely separate analyses to address an independent working hypothesis. All studies were approved by either the Scientific Ethical Committee of Copenhagen and Frederiksberg Municipalities or the Capital Region of Copenhagen (file numbers HA-2009020 and H-2201004, H-32013024, H-16042103, and H-16041794), and conformed to the standards set by the Declaration of Helsinki; no additional ethical approval was necessary for this retrospective study. Subjects or their next-of-kin provided oral and written informed consent prior to inclusion. The data underlying our findings can be shared upon reasonable request directed to the corresponding author of this and the original studies.

Subjects and recordings

The present study encompasses recordings from 48 healthy volunteers, in whom a total of 62 individual baseline periods were recorded; 19 patients with sepsis (34 individual baseline recordings); 36 patients admitted to an intensive care unit with severe TBI recorded a median of 12 (interquartile range, IQR: 11–16) days after the injury (66 individual baseline recordings); and 14 patients admitted to a neurorehabilitation unit 41 (standard deviation, SD: ±12) days after the injury with traumatic (57%) or non-traumatic brain injury (43%) (26 baseline recordings). Baseline recordings were defined as periods before any interventions were initiated. Characteristics of the recordings and studies are provided in Table 1.

Table 1.

Study characteristics.

		N	Age years ±SD	Male n (%)	Recordings n	Length min ±SD	Method	PaCO2 kPa ±SD
Study A 19	Healthy	9	23 ± 2	9 (100%)	9	20 ± 1.8	Mxa	5.4 ± 0.2
–	Sepsis	19	57 ± 14	17 (89%)	34	16 ± 2.3	Mxa	6.2 ± 1.8
Study B 20,21	Healthy	10	23 ± 2	10 (100%)	10	18 ± 1.8	Mxa	5.8 ± 0.3
Study C 22	Healthy	15	31 ± 13	7 (47%)	15	5 ± 0.4	nMxa	–
–	Rehabilitation	14	57 ± 17	7 (50%)	26	6 ± 3	nMxa	–
Study D 18	Healthy	14	28 ± 9	5 (36%)	28	5 ± 0.2	nMxa	–
Study E 23	TBI	36	44 ± 18	10 (28%)	66	6 ± 1.7	nMxa	5.2 ± 0.7

Recordings are baseline periods without any interventions.

N: number of patients; Mxa: Mx using invasively measured arterial blood pressure; nMxa: Mxa using non-invasively measured arterial blood pressure; TBI: traumatic brain injury.

Data collection

Studies A ¹⁹ and B^20,21 recorded invasive ABP in the left radial artery and MCAv by TCD-insonation in healthy volunteers and patients admitted to the intensive care unit with severe sepsis; all subjects were placed in the supine position with slight head elevation (20°). Study C ²² , D, ¹⁸ and E ²³ recorded ABP non-invasively with photoplethysmographic continuous beat-to-beat measurement, and MCAv measured by TCD-insonation while lying supine without head elevation. Recordings from baseline sessions were extracted for all subjects. Arterial carbon dioxide tension (PaCO₂) was extracted when available. Recordings during physiological interventions were also extracted as follows:

• Study A: Induced hypertension during noradrenaline infusion; ¹⁹

• Study B: In the healthy volunteers – four hours after initiation of continuous lipopolysaccharide (LPS) infusion, (1) without and (2) with induced hypertension during noradrenaline infusion; ²¹

• Study C: Head-up tilt (80°); ²² and

• Study D: Head-up tilt (70°). ¹⁸

The data collection is described in full in the original articles.^18–23

Data pre-processing

Recordings were extracted from LabChart (ADInstruments, Sidney, Australia) into a tab-delimited file in the original resolution of 1,000 Hz and were visually inspected for artefacts; periods with artefacts were deleted, ensuring that such periods always started and ended in a nadir. Subsequently, recordings were divided into blocks and epochs using four pre-processing approaches that have been previously reported in the literature^6,17,18 here designated 3-60-F, 6-240-F, 10-300-F, and 10-300-60. For these designations, the first number refers to the duration of each block in seconds, the second number is the duration of each epoch in seconds, and the third number is the duration of the overlaps in seconds, with F indicating an approach where overlaps were not used. Even though the three second block might not be enough to filter out the respiratory component, we have investigated the approach with this block length since it has been used in at least 22 previous publications. ⁶ Mxa was calculated using the clinmon-function from the publicly available R-package ‘clintools’ v. 0.8.2, ²⁴ which generates results comparable to those generated using the ICM+ software (Cambridge Enterprise, Cambridge, United Kingdoms). To ensure sufficient quality of the calculations, blocks were omitted from the analysis if 50% of the raw measurements were missing. Similarly, epochs were omitted if more than 50% of the blocks were missing. A detailed description of the methodology is available in the package documentation and is published elsewhere.^6,24 Pragmatically, we chose to show the 10-300-F in the manuscript and the other approaches in the supplemental material.

The TFA-function from the publicly available R-package ‘clintools’ v. 0.8.2 was used to calculate the TFA-based metrics, focusing on normalised gain, non-nornalised gain and phase in the low frequency range (0.07–0.20 Hz).^13,14 The TFA-function was validated by comparing the results when calculating TFA using the publicly available MatLab-code from David Simpson. ¹³ The function follows the recommendations including application of a coherence threshold identified using 95% confidence limits based on degrees of freedom, and all frequencies with low magnitude-squared coherence are excluded from averaging when calculating the mean values of gain and phase across the bands below this threshold. ¹³

Diagnostic and prognostic performance

The diagnostic performance of Mxa- and TFA-based dynamic cerebral autoregulation metrics was assessed the ability to discriminate between healthy volunteers on one side and patients with sepsis, with severe TBI, and patients admitted to a neurorehabilitation unit, respectively. The prognostic performance was assessed by the ability to predict mortality in patients with sepsis and TBI, and functional outcome for patients with TBI. All these assessments were based on baseline recordings alone.

Interventions

To investigate the potential effect of not having a standardised approach for calculating Mxa, we tried to assess the effect on Mxa in four different contexts (interventions, comparisons, and subjects). The investigation was not carried out to determine potential differences in dynamic cerebral autoregulation, merely to investigate if significance levels could be influenced by the approach chosen. The following were calculated: (1) induced hypertension by noradrenaline infusion compared with baseline in patients with sepsis (from Study A ¹⁹ ); (2) Induced hypertension by noradrenaline infusion compared to baseline in healthy volunteers after LPS infusion (Study B^20,21) (3) Head-up tilt (80°) in healthy volunteers compared to head-up tilt in patients admitted to a neurorehabilitation (Study C ²² ); and (4) head-up tilt (70°) compared to the supine position in healthy volunteers (Study D ¹⁸ ).

Statistical analysis

All statistical analyses were carried out using R 4.0.2 (R Core Team (2020), Vienna, Austria). Normally distributed data are presented as mean (±SD), while non-normally distributed data are presented as median (IQR). The diagnostic and prognostic performance of Mxa and TFA was assessed using receiver operating characteristics (ROC) curves and area under the curve (AUC). The analyses used higher Mxa, lower gain, and higher phase as a predictors of the selected outcome. The AUC will be interpreted as representing ‘no better than chance’ (∼0.5), low accuracy (0.5–0.7), moderate (0.7–0.9), and high accuracy (>0.9).25 Sensitivity analyses were carried out including only Mxa and nMxa, and analyses including only measurements longer than 15 minutes. Students t-test was used to compare groups, and p values calculated without correction for multiplicity. This correction would be relevant if we sought to determine actual significance levels. However, we wanted to exemplify what results could look like based on each approach. Hence, each individual p value is considered to represent the result of an analysis that could be carried out in a separate paper or study.

Results

Patients with sepsis had the highest Mxa compared to the other groups across the four approaches (10-300-F: 0.35 ± 0.34), while healthy subjects (10-300-F: 0.29 ± 0.25) exhibited higher values than both patients admitted to a neurorehabilitation unit (10-300-F: 0.06 ± 0.34) and patients with TBI (10-300-F: 0.09 ± 0.32). Normalised (1.73 ± 1.13) and non-normalised gain (0.93 ± 0.68) was highest in patients with sepsis, while patients admitted to a neurorehabilitation unit had the highest phase (70.12 ± 44.81) (Figure 1, left column; Supplemental Material). PaCO₂ was lower in patients with TBI when compared with healthy volunteers (p = 0.01), and tended to be higher in patients with sepsis than in healthy volunteers (p = 0.06) (Table 1).

Figure 1.

Diagnostic performance of Mxa and transfer function analysis based metrics (one per row) and diagnostic group. Left column: Baseline recordings. Mean and 95% confidence interval is shown. Right column: Receiver operating curves for the discrimination of patient groups with healthy volunteers as the comparator (right column).

Diagnostic performace

The abovementioned patterns were also reflected in the prediction models, where the AUCs for the diagnostic performance of Mxa for patients with sepsis presented with an AUC of 0.54 (95%CI: 0.41–0.67), that of patients with TBI with 0.25 (95%CI: 0.16–0.33), and that of patients undergoing rehabilitation for acquired brain injury ranged with 0.25 (95%CI: 0.14–0.37). Similarly, normalised gain (sepsis: 0.56, 95%CI: 0.43–0.70; TBI: 0.28, 95%CI: 0.19–0.38; Rehabilitation: 0.47, 95%CI: 0.29–0.64), non-normalised gain (sepsis: 0.44, 95%CI: 0.30–0.57; TBI: 0.28, 95%CI: 0.19–0.38; rehabilitation: 0.26, 95%CI: 0.14–0.38), and phase (sepsis: 0.61, 95%CI: 0.48–0.73; TBI: 0.41, 95%CI: 0.31–0.52; rehabilitation: 0.24, 95%CI: 0.09–0.39) presented with an accuracy ‘no better than chance’ (Figure 1, right column, Supplemental Material). The sensitivity analyses, for both Mxa and transfer function analysis based metrics, investigating the diagnostic performance by only including recordings with invasive ABP, only including recordings with non-invasive ABP, and those longer than 15 minutes presented with similar patterns (Supplemental Material).

Prognostic performace

The prognostic performance of Mxa presented with an AUC of 0.59 (95%CI: 0.37–0.81) to predict mortality in patients with sepsis. Similarly prediction of mortality and functional outcome in patients with TBI presented with an accuracy ‘no better than chance’ (mortality, AUC: 0.36, 95% CI: 0.20–0.53; functional outcome, AUC: 0.38, 95%CI: 0.23–0.52). Similarly, normalised gain (sepsis, mortality: 0.29, 95%CI: 0.08–0.51; TBI, mortality: 0.49, 95% CI: 0.31–0.68; TBI, functional outcome: 0.47, 95%CI: 0.30–0.64), non-normalised gain (sepsis, mortality: 0.36, 95%CI: 0.14–0.57; TBI, mortality: 0.49, 95% CI: 0.32–0.66; TBI, functional outcome: 0.45, 95%CI: 0.27–0.62), and phase (sepsis, mortality: 0.59, 95%CI: 0.38–0.80; TBI, mortality: 0.48, 95% CI: 0.29–0.66; TBI, functional outcome: 0.55, 95%CI: 0.35–0.71) presented with an accuracy ‘no better than chance’ (Figure 2, Supplemental Material). The sensitivity analyses, for both Mxa and transfer function analysis based metrics, investigating the prognostic performance by only including recordings with invasive ABP, only including recordings with non-invasive ABP, and those longer than 15 minutes presented with similar patterns (Supplemental Material).

Figure 2.

Prognostic performance of Mxa and transfer function analysis based metrics from baseline recordings grouped by outcome (left column) and metric (one per row), with receiver operating curves with a good outcome or survival as comparators, and the ability to increase Mxa to predict mortality or poor outcome in patients with sepsis and traumatic brain injury (TBI), respectively.

Physiological interventions

The potential influence of non-standardised approach for the calculation of Mxa showed that induced hypertension resulted in a significant decrease in Mxa in patients with sepsis when analysed using 3-60-F (Figure 3(a)) but not with any other approach, while induced hypertension in healthy volunteers during LPS-infusion showed a significant decrease in Mxa for 10-300-F and 10-300-60, but not using 3-60-F and 6-240-F (Figure 3(b)). Mxa during head-up tilt in healthy volunteers was higher than patients in neurorehabilitation for 3-60-F and 6-240-F, while differences were non-significant for 10-300-F and 10-300-60 (Figure 3(c)). Finally, head-up tilt resulted in an increase in Mxa for healthy volunteers for 3-60-F, but not for the rest of the approaches (Figure 3(d)).

Figure 3.

Effect of four different data pre-processing approaches on the estimate of Mxa during (a) induced hypertension (compared to baseline) in patients with sepsis; (b) induced hypertension (compared to baseline) in healthy volunteers after infusion of E. coli lipopolysachharide; (c) Mxa during head-up tilt for healthy volunteers and patients admitted to a neurorehabilitation unit, and (d) the effect of head-up tilt in healthy volunteers. P values were calculated using Student’s t test.

Discussion

This study used recordings from multiple studies to calculate Mxa and TFA measures for different patients and investigated their diagnostic and prognostic performance. Mxa, gain, normalised gain, and phase did not appear to consistently differentiate healthy volunteers from patients with sepsis, with TBI, and those admitted to rehabilitation after acute brain injury; the AUC values indicated ‘no better than chance’ at best. Similarly, they could not predict mortality in patients with sepsis and TBI or functional outcome in patients with TBI. The approach to calculating Mxa affected the level of significance, thereby accentuating importance of standardising this index. Baseline Mxa, normalised gain and non-normalised gain was on average lower and phase higher for patients with TBI compared to healthy volunteers, suggesting better autoregulation in patients with TBI. Cerebral autoregulation is commonly assumed to be intact in healthy volunteers^1,26 and should presumably be comparably worse in patients with acquired brain injury.^27,28 The present finding in itself seems to questions the relevance of TFA and Mxa as measures of dynamic cerebral autoregulation. ³

The present study is not the only one where Mxa in healthy volunteers is around 0.40, ²⁹ nor where patients with TBI present with Mx or Mxa around 0.15.^3,30 The current understanding of Mxa thus conflicts with our findings, which also limits the usefulness of a pre-defined threshold for impaired autoregulation. Indeed, dichotomisation seems inappropriate for this purpose regardless of the chosen threshold. Thus, more than half of our healthy volunteers would have impaired cerebral autoregulation if the predominantly used threshold of 0.3 was used. ⁶ Nonetheless, since Mxa did not differ between the studied patient groups, this could simply be interpreted as there being no difference in their dynamic cerebral autoregulation. This notion is supported by the finding that the well-established TFA-based indices of dynamic cerebral autoregulation were generally also similar between healthy volunteers and the different patient groups.

Mxa also showed chance-results at best in terms of predicting mortality in patients with sepsis and TBI and functional outcome in patients with TBI, findings that were comparable to those obtained when using TFA. Previous studies have reported varying results in terms of the prognostic value of Mx and Mxa between chance-result and moderate accuracy.^5,9,31,32 Ours and these previous findings suggest the degree of impairment of cerebral autoregulation measured by Mxa might not be an optimal marker of functional outcome and survival in these patients. Accordingly, neither Mxa nor TFA measures during the early phase of disease could distinguish between favourable and unfavourable outcomes or between survival and death in these cohorts. Furthermore, all this perhaps puts into question the value of cerebral autoregulation, as measured by TFA and Mxa from a short snapshot data section as a general independent prognostic marker of outcome.

Biomarkers of biological processes should only be used as an endpoint in trials and studies if they are readily measurable, interpretable, reliable, and valid.^33,34 Mxa, which is closely related to Mx but based on ABP rather than CPP, is in principle readily measurable, but as shown in this and previous studies, the approaches to data pre-processing and calculation of Mx and Mxa vary between studies and may affect the results.^6,17,18,35 The repeatability and reproducibility of Mxa between measurement periods and approaches range from poor to moderate;^{17,18,29,36–38} one study showing excellent reliability ⁸ used overlapping periods, which for mathematical reasons should yield an optimal reliability. However, the data pre-processing before calculation of Mxa directly affected the results, i.e. Mxa showed a significant change or difference for some approaches and not for others, thus fundamantally questioning both the reliability of this index. Furthermore, our findings highlight that the interpretation of Mxa is complicated by the fact that the physiological mechanism that Mxa is actually depicting is unclear.

Strengths and limitations

Although the overall samples site is relatively large, each subgroup's size is rather limited, which increases the risk of a type II error. Previous studies with more than 150 patients with TBI have been able to show statistical significant difference for Mx and Mxa when comparing favourable and unfavourable outcome.^31,39 However, even when investigating more than 150 patient with TBI comparison between these groups can result in insigficant difficerence. ⁴⁰ Nonetheless, the imprecision caused by the rather small sample size is somewhat accounted for when interpreting AUC using 95% confidence interval. This study was limited by the retrospective design, thus limiting the possibility to obtain long recordings which would stabilise Mxa. ⁶ However, the majority of our recordings were still longer than the suggested 6 minutes needed for Mxa to stabilise, ⁴¹ and longer than the suggested 5 minutes for calculation of TFA. ¹³ We further addressed this issue by making a sensitivity analysis of recordings longer than 15 minutes, and still saw a similar pattern. Another limitation is the use of recordings using both non-invasive, and invasive measurement of ABP. ⁴² The potential difference between Mxa calculated using non-invasive and invasive ABP is not fully understood.^35,43,44 Furthermore, especially for Mxa, the missing measure of ICP could have influenced the results; however, a previous investigation showed that TFA exhibits moderate to excellent reliability when comparing measures generated with ABP and CPP in patients with subarachnoid haemorrhage. ³⁵ Finally, the actual influence of PaCO₂ is unclear in relations to Mxa; however, previous reports suggest that higher PaCO₂ increases Mx which could influence our findings.^45,46

Conclusion

Contrary to previous studies, the diagnostic and prognostic performance of both Mxa- and TFA-based dynamic cerebral autoregulation metrics in our hands appears to be questionable. Furthermore, the specific approach for data pre-processing for Mxa appears to have a substantial impact on the results.

ORCID iD

Markus Harboe Olsen https://orcid.org/0000-0003-0981-0723